NUMERICAL ALGORITHM USING MULTIZONE ADAPTIVE GRID GENERATION FOR MULTIPHASE TRANSPORT PROCESSES WITH MOVING AND FREE BOUNDARIES

References

• H. Zhang and M. K. Moallemi , A Multizone Adaptive Grid Generation Technique for Simulation of Moving and Free Boundary Problems , Numer. Heat Transfer, Part B , vol. 27 , pp. 255 – 276 , 1995 .
   Web of Science ®Google Scholar
• R. Viskanta , Heat Transfer during Melting and Solidification of Metal , J. Heat Transfer , vol. 110 , pp. 1205 – 1219 , 1988 .
   Web of Science ®Google Scholar
• J. Crank , Free and Moving Boundary Problems , Clarendon Press , Oxford , 1984 .
   Google Scholar
• A. A. Samarskii , P. N. Vabishchevich , and O. P. Iliew , Numerical Simulation of Convection/Diffusion Phase Change Problems-A Review , Int. J. Heat Mass Transfer , vol. 36 , pp. 4095 – 4106 , 1993 .
   Web of Science ®Google Scholar
• C. Beckermann and R. Viskanta , Natural Convection Solidsol;Liquid Phase Change in Porous Media , Int. J. Heat Mass Transfer , vol. 31 , pp. 35 – 46 , 1988 .
   Web of Science ®Google Scholar
• V. R. Voller , M. Cross , and N. C. Markatos , An Enthalphy Method for Convection Diffusion Phase Change , Int. J. Numer. Meth. Eng ., vol. 24 , pp. 271 – 284 , 1987 .
   Web of Science ®Google Scholar
• W. Y. Raw and S. L. Lee , Application of Weighting Function Scheme on Convection–Conduction Phase Change Problems , Int. J. Heat Mass Transfer , vol. 34 , pp. 1503 – 1513 , 1991 .
   Web of Science ®Google Scholar
• W. Shyy and M.-H. Chen , Steady-State Natural Convection with Phase Change , Int. J. Heat ass Transfer , vol. 33 , pp. 2545 – 2563 , 1990 .
   Web of Science ®Google Scholar
• w. D. Bennon and F. P. Incropera , A Continuum Model for Momentum, Heat, and Species Transport in Binary Solid-Liquid Phase Change Systems. I. Model Formulation , Int. J. Heat Mass Transfer , vol. 30 , pp. 2161 – 2170 , 1987 .
   Web of Science ®Google Scholar
• H. Zhang , M. K. Moallemi , and S. Kumar , Analytical and Numerical Modeling of the Dip-Coating Process , J. Heat Transfer , vol. 115 , pp. 453 – 460 , 1993 .
   Web of Science ®Google Scholar
• C. F. Hsu , E. M. Sparrow and S. V. Patankar , Numerical Solution of Moving Boundary Problems by Boundary Immobilization and a Control-Volume-Based Finite Difference Scheme , Int. J. Heat Mass Transfer , vol. 24 , pp. 1335 – 1343 , 1981 .
   Web of Science ®Google Scholar
• N. Ramachandran , J. P. Gupta , and Y. Jaluria , Thermal and Fluid Flow Effects during Solidification in a Rectangular Enclosure , Int. J. Heat Mass Transfer , vol. 25 , pp. 187 – 194 , 1982 .
   Web of Science ®Google Scholar
• M. Lacroix , Effects of Buoyancy and Surface Tension Forces on the Melting of a Metal , Numer. Heat Transfer, Part A , vol. 19 , pp. 101 – 115 , 1991 .
   Web of Science ®Google Scholar
• M. R. Albert and K. O'Neill , Transient Two-Dimensional Phase Change with Convection Using Deforming Finite Elements , in R. W. Lewis, K. Morgan, J. A, Johnson, and W. R. Smith (eds.) , Computer Techniques in Heat Transfer , vol. 1 , Pineridge Press , Swansea , 1985 .
   Google Scholar
• H. Zhang and M. K. Moallemi , Numerical Simulation of Hot-Dip Metallic Coating Process , Int. J. Heat Mass Transfer , vol. 38 , pp. 241 – 257 , 1995 .
   Web of Science ®Google Scholar
• C. Hirsch , Numerical Computations of Internal and External Flows, Volume 1 Fundamentals of Numerical Discretization , pp. 161 – 264 , John Wiley , New York , 1988 .
   Google Scholar
• H. Zhang , A Multizone Adaptive Grid Generation Technique for Simulations of Moving and Free Boundary Problems , Doctoral dissertation , Polytechnic University , Brooklyn , 1993 .
   Google Scholar
• K. C. Karki and S. V. Patankar , Calculation Procedure for Viscous Incompressible Flows in Complex Geometries , Numer. Heat Transfer , vol. 14 , pp. 295 – 307 , 1988 .
   Web of Science ®Google Scholar
• C. J. Kim and M. Kaviany , A Numerical Method for Phase Change Problems with Convection and Diffusion , Int. J. Heat Mass Transfer , vol. 35 , pp. 457 – 467 , 1992 .
   Web of Science ®Google Scholar
• S. Majumdar , Role of Underrelaxation in Momentum Interpolation for Calculation of Flow with Nonstaggered Grids , Numer. Heat Transfer , vol. 13 , pp. 125 – 132 , 1988 .
   Web of Science ®Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , McGraw-Hill , New York , 1980 .
   Google Scholar
• T. H. Kuehn and R. J. Goldstein , An Experimental Study of Natural Convection in Concentric and Eccentric Horizontal Cylindrical Annuli , J. Heat Transfer , vol. 100 , pp. 635 – 640 , 1978 .
   Web of Science ®Google Scholar
• F. Wolff and R. Viskanta , Solidification of a Pure Metal at a Vertical Wall in the Presence of Liquid Superheat , Int. J. Heat Mass Transfer , vol. 31 , pp. 1735 – 1744 , 1988 .
   Web of Science ®Google Scholar
• M. N. Ozisik , Heat Conduction , John Wiley , New York , 1980 .
   Google Scholar
• O. Adetutu and V. Prasad , Melting in Rectangular and Cylindrical Cavities Effects of Curvature, Aspect Ratio and Buoyancy Forces, Advanced Computations in Materials Processing , ASME HTD-vol. 241 , pp. 45 – 56 , 1992 .
   Google Scholar
• C. J. Ho and R. Viskanta , Experimental Study of Solidification Heat Transfer in an Open Rectangular Cavity , J. Heat Transfer , vol. 105 , pp. 671 – 673 , 1983 .
   Web of Science ®Google Scholar
• C. J. Kim and S. T. Ro , Shrinkage Formation during the Solidification Process in an Open Rectangular Cavity , J. Heat Transfer , vol. 115 , pp. 1078 – 1081 , 1993 .
   Web of Science ®Google Scholar
• H. Zhang , V. Prasad , and M. K. Moallemi , A Solution Adaptive Scheme for Deformable Free Surface Flow and Heat Transfer Problems , ASME HTD-vol. 311 , pp. 119 – 127 , 1995 .
   Google Scholar
• H. Zhang and V. Prasad , A Multizone Adaptive Process Model for Czochralski Crystal Growth at Low and High Pressures , J. Crystal Growth , vol, 155 , pp. 47 – 65 , 1995 .
   Web of Science ®Google Scholar
• D. T. J. Hurle and B. Cockayne , Czochralski Growth , in D. T. J. Hurle (ed.) , Bulk Crystal Growth , pp. 99 – 211 , North-Holland , New York , 1994 .
   Google Scholar
• F. Dupret and N. V. D. Bogaert , Modeling Bridgman and Czochralski Growth , in D. T. J. Hurle (ed.) , Bulk Crystal Growth , pp. 875 – 1013 , North-Holland , New York , 1994 .
   Google Scholar
• J. J. Derby and R. A. Brown , Thermal-Capillary Analysis of Czochralski and Liquid Encapsulated Czochralski Crystal Growth , J. Crystal Growth , vol. 74 , pp. 605 – 624 , 1986 .
   Web of Science ®Google Scholar
• H. Kopetsch , Numerical Simulation of the Czochralski Bulk Flow of Silicon on a Domain Confined by a Moving Crystal-Melt Interface and a Curved Melt-Gas Meniscus , PCH PhysicoChem. Hydrodynam ., vol. 11 , pp. 357 – 375 , 1989 .
   Google Scholar
• J. U. BrackbiU and J. S. Saltzman , Adaptive Zoning for Singular Problems in Two Dimensions , J. Comput. Phys ., vol. 46 , pp. 342 – 368 , 1982 .
   Web of Science ®Google Scholar
• A. Anselmo , V. Prasad , J. Koziol , and K. P. Gupta , Oscillatory convection in Low Aspect Ratio Czochralski Melts , J. Crystal Growth , vol. 134 , pp. 116 – 141 , 1993 .
   Web of Science ®Google Scholar